Correct Thinking

Dilemma

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4.Dilemma – a syllogism that is both conditional and disjunctive. The major premise is a compound conditional proposition consisting of two or more simple conditional propositions connected by and or its equivalent. The minor premise is a disjunctive proposition that alternatively posits the antecedents (constructive dilemma), or sublates the consequents )destructive dilemma), of each of these simple conditional propositions.

CONSTRUCTIVE DILEMMA

The disjunctive propositions posits the antecedent of the conditional propositions; the conclusion posits their consequents.

1.SIMPLE CONSTRUCTIVE

2.COMPLEX CONSTRUCTIVE

Either A or B

But, if A, then Z; if B, then Z.

Therefore Z.

Either A or B.

But, if A, then X; if B, then Y.

Therefore either X or Y.

DESTRUCTIVE DILEMMA

The disjunctive proposition sublates the consequents of the conditional propositions; the conclusion sublates their antecedents.

1.SIMPLE DESTRUCTIVE

2.COMPLEX DESTRUCTIVE

If A, then X and Y

But, either not X or not Y.

Therefore not A.

If A then X; and if B, then Y.

But, either not X or not Y.

Therefore either not A or not B.

In the simple constructive dilemma, the conditional premise infers the same consequent from all the antecedents presented in the disjunctive propositions. Hence, if any antecedent is true, the consequent must be true. This form is illustrated by the reflections of a man trapped in an upper story of a burning building.

I must either jump or stay – there is no other alternative.

But if I jump, I shall die immediately from the fall.

And if I stay I shall die immediately from the fire.

Therefore I shall die immediately.

In the complex constructive dilemma, the conditional premise infers a different consequent from each of the antecedents presented in the disjunctive proposition. If any antecedent is true, its consequent is likewise true. But since the antecedents are posited disjunctively and, since different consequent flows from each of them, the consequents must likewise be posited disjunctively. The men who brought to Jesus the woman caught in adultery had this form of dilemma in mind.

Jesus will either urge that she be stoned to death or that she be released

without stoning.

But if he urges the first, he will make himself unpopular with the people

because of his severity.

And if he urges the second, he will get into trouble with the Jewish

authorities for disregarding the law of Moses.

Therefore he will either become popular with the people or get into trouble

with the Jewish authorities.

In the simple destructive dilemma, the conditional premise infers more than one consequent from the same antecedent. If any of the consequents is false, the antecedent is false. Hence, since the disjunctive sublates the consequents alternatively, at least one of them must be false, and consequently the antecedent must also be false. This type is not distinct from a conditional syllogism in which the consequent is sublated in the minor premise and the antecedent is sublated in the conclusion. Still, on account of the disjunctive premise, it is generally called a dilemma.

If I am to pass the examination, I must do two things: I will study all night

and I must also be mentally alert as I write.

But either I will not study all night or I will not be mentally alert as I write.

Therefore I will not pass the examination.

In the complex destructive dilemma, the conditional premise infers a different consequent from each antecedent. The disjunctive premise sublates these consequents alternatively, and the conclusion sublates their antecedents alternatively.

If John were wise, he would not speak irreverently of holy things in jest;

and if he were good, he would not do so in earnest.

But he does it either in jest or in earnest.

Therefore John is either not wise or not good.

The dilemma is subject to the following rules:

Rule 1: The disjunctive must state all pertinent alternatives.

Rule 2: The consequent in the conditional proposition must flow validly

from the antecedents.

Rule 3: The dilemma must not be subject to rebuttal.

The alternatively presented in a dilemma are called horns and that a dilemma is sometimes called a syllogismus cornutus or a horned argument. If you show that the first rule us violated, you escape between the horns of the argument.

Sorites

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3.Sorites – a polysyllogism consisting of a series of simple syllogisms whose conclusions, except for the last, are omitted. There are two special rules of the sorites:

Rule 1: All but the last premise must be affirmative. If a premise is negative, the conclusion must be negative.

A is B

B is C

C is D

D is (not) E

----------------

A is (not) E

Rule 2: All but the first premise must be universal. If the first premise is particular, the conclusion must be particular.

(some) A is B

B is C

C is D

D is (not) E

--------------------------------

(some) A is (not) E

The human soul is endowed with intellect and will.

What is endowed with intellect and will is spiritual.

What is spiritual is incorruptible.

What is incorruptible is immortal.

Therefore, the human soul is immortal.

Epichereme

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2.Epichereme – a syllogism in which a proof is joined to one or both of the premises. The proof is often expressed by a casual clause. The premise to which a proof is annexed is an enthymeme.

major premise: If man has spiritual activities, he has a spiritual soul,

because every activity requires an adequate principle.

minor premise: But since man knows immaterial things; man has spiritual activities.

conclusion: Therefore man has a spiritual soul.

Enthymeme

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1.Enthymeme – a syllogism in which one of the premises or the conclusion is

omitted. There are three orders of enthymeme:

a.first order: when the major premise is omitted – The human soul is spiritual

and therefore immortal.

b.second order: when the minor premise is omitted – What is spiritual is

immortal and for this reason the human soul is immortal.

c.third order: when the conclusion is omitted – The human soul is spiritual and

whatever is spiritual is immortal.

What is spiritual is immortal

The human soul is spiritual.

Therefore, the human soul is immortal.

Ordinary Language Arguments

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Many categorical syllogisms that are not in standard form as written can be translated into standard form syllogism. The goal is to produce an argument consisting of three standard form categorical propositions that contain a total of three different terms, each of which is used twice in distinct propositions. Since this task involves not only the translation of the component statements into standard form but the adjustment of these statements one to another so that their terms occur in matched pairs, a certain amount of practice is usually required before it can be done with any facility. In reducing the terms to three matched pairs it is often helpful to identify some factor common to two or all three propositions and express this common factor through the strategic use of the parameters. Consider the following argument:

Henry must have overslept this morning because he was late for work,

and is never late for work unless he oversleeps.

All three statements are about Henry, but if the parameter “persons identical to Henry” were selected it would have to be used more than twice. The temporal adverbs in the argument “this morning” and “never,” suggest that “times” might be used. Following this suggestion, we have:

All times identical to this morning are times Henry overslept, because all times identical to this morning are times Henry is late for work, and all times Henry is late for work are times Henry overslept.

We now have a standard form categorical syllogism. If we adopt the following convention,

A = times identical to this morning

B = times Henry overslept

C = times Henry is late for work

The syllogism may then be symbolized as follows:

All C are B. All times Henry is late for work are times Henry overslept

All A are C. All times identical to this morning are times Henry is late for work.

All A are B. Therefore, all times identical to this morning are times Henry overslept.

Conjunctive Syllogism

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4.Conjunctive Syllogism – A syllogism whose major premise is a conjunctive proposition, the minor premise posits one member of the major, and whose conclusion sublates the other member of the major. There is only one valid procedure: to posit one member in the minor premise and sublate the other in the conclusion.

The criminal could not be in Manila and Baguio at the same time;

But he was in Manila;

Therefore he could not be in Baguio.

[The criminal could not be in Manila and Baguio at the same time;

But he was not in Manila;

Therefore he was in Baguio.]

Disjunctive Syllogism

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3.Disjunctive Syllogism – A syllogism whose major premise is a disjunctive proposition.

a.It is a strict disjunctive if only one among the alternatives enumerated in

the major premise is true. For the disjunctive syllogism in the strict sense

the following rules are applicable:

Rule 1: If the minor premise posits one or more members of the

major premise, the conclusion must sublate each of the other

members.

It is either A or B. It is either A or B or C.

But it is A. But it is A.

Therefore it is not B. Therefore it is neither B nor C.

Rule 2: If the minor premise sublates one or more of the members

of the major premise, the conclusion posits the remaining

members, one of which must be true.

It is either A or B. It is either A or B or C.

But it is not A. But it is not A.

Therefore it is B. Therefore it is either B or C.

b.It is a broad disjunctive if at least one alternative among those

enumerated in the major premise is true but more may be true. In a

disjunctive syllogism in the broad sense, the major premise is a

disjunctive proposition in the broad sense. There is only one valid

procedure: to sublate one (or more – but not all) of the members in the

minor and posit the remaining member or (members) in the conclusion.

If more than one member remains, the conclusion itself must be a

disjunctive proposition in the broad sense.

It is either A or B or C or D – at least one of them

But it is neither A nor B;

Therefore it is either C or D – at least one of them.

Conditional Syllogism

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2.Conditional Syllogism – a syllogism whose major premise is a conditional proposition. It is a mixed conditional syllogism if the minor premise is a conditional proposition or a pure conditional syllogism if both premises are conditional propositions.

a.The mixed conditional syllogism is governed by the two laws that governed relationship between the antecedent and the consequent.

1.If the antecedent is true and the sequence valid, the consequent

is true.

2. If the consequent is false and the sequence valid, the antecedent

Is false.

When applied to the mixed conditional syllogism, these general rules are

expressed thus:

If the antecedent is posited or affirmed in the minnow premise, then the consequent is also posited or affirmed in the conclusion.

VALID

If A then B

But A

Therefore B

INVALID

If A then B

But not A

Therefore not B

If the consequent is sublated or denied in the minor premise then the antecedent is sublated or denied in the conclusion.

VALID

If A then B

But not B

Therefore not A

INVALID

If A then B

But not B

Therefore not A

b.The purely conditional syllogism, which has conditional syllogism, which has conditional propositions for both its premises, has exactly the same forms and the same rules as the mixed conditional syllogism except that the condition expressed in the minor premise must be retained in the conclusion.

If A is B, then C is D;

But if X is Y, then A is B;

Therefore if X is Y, then C is D.

If A is B, then C is D;

But if X is Y, then C is not D;

Therefore if X is Y, then A is not B.

If he has terminal cancer, then he is seriously ill.

But if he is undergoing chemotherapy, then he has terminal cancer.

Therefore if he is undergoing chemotherapy, then he is seriously ill.

If he has terminal cancer, then he is seriously ill.

But if he can go about his daily work, then he is not seriously ill.

Therefore if he can go about his daily work, he has no terminal cancer.

Hypothetical Propositions

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A hypothetical syllogism is a syllogism that has a hypothetical proposition as one of its premises.

1.Hypothetical Propositions – A hypothetical proposition is one whose predicate does not assert of the subject in an absolute manner. There are three kinds of hypothetical propositions:

a.conditional (if…, then…) – the assertion of the consequent is dependent upon

the condition established by the antecedent.

If the elections will not push through then there will violence in the country.

b.disjunctive (either…, or…) – affirms the possibility of one or more of the

alternatives.

A candidate for public office is either qualified on unqualified.

c.conjunctive (not both…, and…) – denies the simultaneous possibility of both

alternatives.

The farmer cannot be environment friendly and not environment friendly at the

same time.

Rules of Syllogism

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Rules of Syllogism – There are five rules that govern the categorical syllogism:

Rule 1: There must be three terms and only three – the major term, the minor term, and the middle term. If there are only two terms the relationship between these two cannot be established. And if there were more than three terms this would violate the structure of the categorical syllogism.

Animals are living beings.

Plants are heavenly bodies.

Therefore…

Stones are minerals.

Minerals are stones.

Therefore…

A widower is a man.

A man is either male or female.

Therefore, a widower is either male or female.

Rule 2: Each term must occur twice in the syllogism: the major must occur in the conclusion and in one premise, the minor in the conclusion and in one premise; the middle in both premise but not in the conclusion. There must therefore be a total of three propositions in the syllogism.

Rule 3: The middle term must be distributed at least once. If the middle term is particular in both premises it might stand for a different portion of its extension in each occurrence and thus be equivalent to two terms.

All sharks are fish.

All salmon are fish.

Therefore, all salmons are sharks.

Many rich men oppress the poor.

Jones is a rich man.

Therefore, Jones oppresses the poor.

Rule 4: The major and minor terms may not be universal in the conclusion unless they are universal in the premises. If a term is distributed in the conclusion then it must be distributed first in the premise.

There is an illicit major term if the major term is universal in the conclusion but particular in the premise:

All horses are animals.

All dogs are not horses.

Therefore, all dogs are not animals.

There is an illicit minor term if the minor term is universal in the conclusion but particular in the premise:

All tigers are mammals.

All mammals are animals.

Therefore, all animals are tigers.

The rationale behind this rule is that we may not conclude about all the inferiors of a term if the premises have given us information about only some of them. The key to detect a violation of this rule is to examine the conclusion. If there is no term that is distributed in the conclusion then this rule could not have been violated. If one or both terms in the conclusion are distributed there is possibility of the rule having been violated. If a term is distributed both in the premise and the conclusion there is no violation of this rule.

Rule 5: If both premises are affirmative, the conclusion must be affirmative. The reason for this rule is that affirmative premises either unite the minor or major terms, or else do not bring them into relationship with each other at all.

All sins are detestable.

All pretenses are a sin.

Therefore, all pretenses are not detestable.

There is a need to be cautious about apparently affirmative or negative propositions:

Animals differ from angels.

Man is an animal.

Therefore, a man is not a horse.

Rule 6: If one premise is affirmative and the other negative, the conclusion must be negative.

All crows are birds.

All wolves are not crows.

Therefore, all wolves are birds.

Some premises are apparently affirmatives but actually negative and therefore yield a valid conclusion:

Dogs are not cats.

Greyhounds are dogs.

Therefore, greyhounds differ from cats.

Rule 7: If both premises are negative – and not equivalently affirmative – there can be no conclusion.

Reptiles are not mammals.

Dogs are not reptiles.

Therefore…

Rule 8: If both premises are particular there can be no conclusion.

Structure of Syllogism

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A syllogism is a deductive argument cocsisting of two premises and one conclusion. It is called a categorical syllogism if all the propositions are categorical propositions.

Structure of the Syllogism – The propositions must contain a total of three terms. A synonym introduced into one of the propositions does not add another term into the syllogism.

All philanthropists are wealthy persons.

No wealthy persons are selfish.

Therefore, no philanthropists are selfish.

All businessmen are wealthy persons.

All rich persons are hardworking individuals.

Therefore, all businessmen are hardworking individuals.

Each of the terms must be used in the same sense throughout the syllogism. If a term is used in different senses it would not count as one term and so there will result more than three terms.

The poor need government subsidy.

These students are poor.

Therefore, these students need government subsidy.

The propositions need to be in their standard form; however, analysis is greatly simplified if the propositions are in standard form.

The three terms of the categorical syllogism are the major term, the minor term, and the middle term. The major term is the predicate of the conclusion. The minor term is the subject of the conclusion. And the middle term is that which provides the linkage between the two premises. It is thus found in both premises but never in the conclusion. A premise is designated as major or minor depending on the term it carries.

The categorical syllogism is in a standard logical form when the premises are strictly categorical propositions, the two usages of each term are identical, and the major premise is listed first followed by the minor premise and then the conclusion.

Equivalence of Propositions

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Equivalence of Propositions – the formulation of a new proposition, with the same meaning as the original, by interchanging the subject and predicate terms of the latter and/or by the use or removal of negatives.

1. conversion – interchanging the subject and predicate terms of the original but leaving its quality unchanged.

convertend

original proposition

S is P

converse

resultant proposition

Ps is Sp

1.a. simple done by simply interchanging subject and predicate terms because they have the same quantity. Note that the quantity of the converse should be the same as the quantity of the convertend.

E – E	No dog is a cat – No cat is a dog.
I - I	Some pictures are clear prints – Some clear print are pictures.

1.b. partial – the unioversal quantity of the convertend becomes particular in the converse.

A – I

All horses are animals – Some animals are horses.

It is advisable to reduce a proposition to its logical form before attempting conversion. Simple conversion is applied to a singular proposition whose predicate is also singular.

2. obversion – formulating a new proposition [obverse] by retaining the subject term and quantity of the original proposition [obvertend], changing its quality, and using as predicate term the contradictory of the original predicate term. The procedure for obversion is as follows:

1. Retain the subject quality of the obvertend.

2. Change the quality.

3. As new predicate, use the contradictory of the predicate of the obvertend.

A – E	All me are sinful.	-	All me are not sinless.
I - O	Some house are white.	-	Some houses are not non-white.
E – A	No person is indispensable.	-	All persons are dispensable.
O - I	Some jewels are not rare.	-	Some jewels are non-rare.

3. contraposition – the formulation of a new proposition [contraposit] whose subject is the contradictory of the predicate of the original proposition [contraponend]. There are two types of contraposition and the corresponding procedures are as follows:

Type 1:

1. Obvert

2. Convert the obverse.

[contraponend] A - E [contraposit]

E - I

O - I

A - E
Every dog is an animal.	Every dog is not a non-animal.	Every non-animal is a dog.
E - I
No dog is a cat.	All dogs are non-cats.	Some non-cats are dogs.
O - I
Some men are not voters.	Some men are non-voters.	Some non-voters are men.

Type 2:

1. Obvert.

2. Convert the obverse.

3. Then obvert the converse of the obverse.

[contraponend] A - A [contraposit]

E - O

O - I

A - A
Every man is mortal.	Every man is not immortal.	Every immortal is not a man.	Every immortal is a non-man.
E - O
No dog is a cat.	All dogs are non-cats.	Some non-cats are dogs.	Some non-cats are not non-dogs.
O - I
Some men are not voters.	Some men are non-voters.	Some non-voters are men.	Some non-voters are not non—men.

Opposition of Proposition

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Opposition of Proposition – the difference as to quantity or quality or both of two propositions having the same subject term and predicate term.

contradictory – difference of two propositions as to quantity and quality such that one is necessarily the negation of the other. Both cannot be true but both cannot be false.

If one is true, the other is false and vice-versa

A vs O

E vs I

contrary – difference as to quality of two universal propositions. Both cannot be true but both can be false.

If one is true, the other is false; if one is false the other is

doubtful.

A vs E

subcontrary – difference of two particular propositions as to quality. Both can be true but both cannot be false.

If one is false the othet is true; if one is true the other is

doubtful.

I vs O

subalternate – difference as to quantity of two propositions having the same quality, between a universal proposition (superaltern) and its corresponding particular (subaltern).

If the superaltern is true, the subaltern is also true but not

vice-versa. If the subaltern is false, the superaltern is also

false but not vice-versa.

A vs I

E vs O

A being true	E is false	I is true	O is false
E being true	A is false	I is false	O is true
I being true	E is false	A is doubtful	O is doubtful
O being true	A is false	E is doubtful	I is doubtful
A being false	O is true	E is doubtful	I is doubtful
E being false	I is true	A is doubtful	O is doubtful
I being false	A is false	E is true	O is true
O being false	A is true	E is false	I is true

Classification of Proposition

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Classification of Propositions – There are four kinds of categorical propositions:

those that assert that the whole subject class included in the predicate class;
those that assert that the whole subject class is excluded from the predicate class;
those that assert that part of the subject class is included in the predicate; and,
those that assert that part of the subject class is excluded from the predicate class.

A	Universal-Affirmative	All S are P	All politicians are honorable men.
E	Universal-Negative	All S are not P	All politicians are not honorable men.
I	Particular-Affirmative	Some S are P	Some politicians are honorable men.
O	Particular-Negative	Some S are not P	Some politicians are not honorable men.

Form A	All S are P asserts that the predicate is affirmed of all members of S, the subject category.
Form E	No S are P asserts that the predicate is denied of all members of S.
Form I	Some S are P asserts that there is at least one member of S and the predicate is affirmed of it.
Form O	Some S are not P asserts that there is at least one of S and the predicate is denied of it.

All S are P	Every member of the S class is a member of the P class; that is, the S class is included in the P class.
No S are P	No member of the S class is a member of the P class; that is, the S class is excluded from the P class.
Some S are P	At least one member of the S class is a member of the P class.
Some S are not P	At least one member of the S class is not a member of the P class.

Standard Categorical Format

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Standard Categorical Format – translating ordinary language statements into categorical form. While few statements in ordinary written and oral expression are categorical propositions in standard form, many of them can be translated into standard form propositions. The necessity for this translation is twofold: the first is that the operations and inference pertinent to standard form categorical propositions become applicable to these statements, and the second is that such statements, once translated are completely clear and unambiguous as to their meaning. The simple rule for this translation is to understand the meaning of the given statement and then reformulate it in a new statement that has a quantifier, subject term, copula, and predicate term.

a. terms without nouns – The subject and predicate terms of a categorical proposition must contain either a noun or noun substitute that serves to denote the class indicated by the term. Nouns and noun substitute denote classes, while adjectives connote attributes. If a term consists of only an adjective, a noun or noun substitute should be introduced to make the term genuinely denotative.

Some rose are red.	Some roses are red flowers.
All tigers are carnivorous.	All tigers are carnivorous animals.

b. nonstandard verbs – statements in ordinary usage often incorporate other forms of the verb to be. Such statements may be translated according to the following examples:

Some persons who go to college will become educated.	Some persons who go to college are persons who will be educated.
Some dogs would rather bark than bite.	Some dogs are animals that would rather bark than bite.

singular proposition – A singular proposition makes an assertion about a specific person, place, thing, or time. Singular propositions are typically translated into universals by means of a parameter, a phrase that when introduced into a statement affects the form but not the meaning. Some parameters that may be used to translate singular propositions are: persons identical to, place identical to, things identical to, times identical to.

Gloria Macapagal-Arroyo is the president of this country.	All persons identical to Gloria Macapagal-Arroyo are the president of this country.
There is a radio in the back bedroom.	All places identical to the back bedroom are places where there is a radio.

adverbs and pronouns – when a statement contains a spatial adverb such as where, wherever, anywhere, everywhere, or nowhere, or a temporal adverb such as when, whenever, anytime, always, or never, it may be translated in terms of places or times, respectively. a statement containing pronouns such as who, whoever, anyone, what, whatever, or anything may be translated in terms of persons or things, respectively.

He is always clean shaven.	All times are times he is clean shaven.
Whoever works hard will succeed.	All persons who work hard are persons who will succeed.

unexpressed quantifiers – many statements in ordinary usage have quantifiers that are implied but not expressed. In introducing the quantifiers one must be guided by the most probable meaning of the statement.

Emeralds are green gems.	All emeralds are green gems.
Children live next door.	Some children live next door.

nonstandard quantifiers – sometimes the quantity of the statement is indicated by a word or words other than the three quantifiers that are allowed.

A few soldiers are heroes.	Some soldiers are heroes.
Anyone who voted is a citizen.	All voters are citizens.

conditional statements – when the antecedent and consequent of a conditional statement talk about the same thing, the statement can usually be translated into categorical form.

If it is a mouse, then it is a mammal.	All mice are mammals.
If an animal has four legs, then it is not a bird.	No four-legged animals are birds.

In translating conditional statements it is sometimes useful to employ a rule called transposition. According to this rule, the antecedent and consequent of a conditional statement may switch places if both are negated. For example, the statement If something is not valuable, then it is not scarce is logically equivalent to If something is scarce, then it is valuable. This is then translated as All scarce things are valuable things.

The word unless means if…not. For example, the statement A car will not run unless there is gas in the tank means A car will not run if there is not gas in the tank which means If there is not gas in the tank, then a car will not run. by transposition, this means, If a car runs, then there is gas in the tank which is translated as All cars that run are cars with gas in the tank.

exclusive propositions – propositions that involve the words only, none but, none except, and no… except are exclusive propositions. Efforts to translate them into categorical propositions frequently lead to confusion of the subject term with the predicate term. Such confusion can be avoided if the statement is phrased as a conditional statement first, then as a categorical statement. For example, the statement Only executives can use the silver elevator is equivalent to If a person can use the silver elevator, he is an executive. The correct categorical proposition is All persons who can use the silver elevator are executives.

Only elected officials will attend the convention.

When only and none but occur in the middle of a statement, the statement must first be restructured so that the term preceded by only or none but occurs first. Then the statement can be translated as those above. For example, the statement Executives can use only the silver elevator is equivalent to Only the silver elevator can be used by executives. This, in turn, is equivalent to If an elevator can be used by executives, which is translated: All elevators that can be used by executives are elevators identical to the silver elevator.

He owns only the shirt on his back.

All things owned by him are things identical to the shirt on his back.

Statements beginning with the words the only are translated differently from those beginning with only. For example, the statement The only cars that are available are Chevrolets means that If a car is available, then it is a Chevrolet. This, in turn, is translated as All cars that are available are Chevrolets. In other words, the only, when it occurs at the beginning of a statement, can simply be replaced with all, and the order of the term is not reversed in the translation. When the only occurs in the middle of a statement, the statement must be restructured so that it occurs at the beginning. For example, Romances are the only books he sells is equivalent to The only books he sells are romances. This is then translated as All books that he sells are romances.

Accountants are the only ones who will be hired.

All those who will be hired are accountants.

exceptive propositions – propositions of the form All excepts S are P and All but S are P are exceptive propositions. They must be translated not as single categorical propositions but as pairs of conjoined categorical propositions. Statements that include the phrase none except, on the other hand, are exclusive and not exceptive propositions.

All except students are invited.

No students are invited persons + All non-students are invited persons.

Categorical Proposition

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Logic originated with the Greek philosophers. As far back as seven hundred years BC, they already had an understanding of good argument and used reasoning to draw abstract conclusions. This can be gleaned from fragments of their writings. But it was Aristotle who first developed a logical system. His comprehensive theory includes precise definitions, principles of reasoning, a system for exposing arguments, and rules for evaluating reasoning. The Aristotelian system is called categorical logic. It is also known as deductive logical system. It is a method for analyzing deductive argument which Aristotle called syllogisms. One of the requirements of categorical logic is that statement follows a certain form. They have to be categorical statements and must assert a relationship between one group of things and another.

Categories are classes or group of things. The words and phrases used to refer or name categories are called terms.

Statements in categorical logic assert a relationship between one category, the subject category, and another, the predicate category. The statement “all men are good” is thus to be interpreted as meaning that “all those belonging to the category of man belong to the category of good”. For Aristotle all statements can be expressed in terms of categories and the assertion of a relationship between categories. And all reasoning in categorical logic is reasoning about categories.

ORDINARY STATEMENT	CATEGORICAL STATEMENT
Some dogs bark.	At least one member of the class of dogs is a member of the class of animals that bark.
All spiders have eight legs.	All members of the class of spiders are members of the class of things having eight legs.
No bankers favor the withholding of interest on savings account.	No member of the class of bankers are members of the class of person favoring withholding interest on savings account.
Some of the people are not for the death penalty.	At least one member of the class of people is not a member of the class of those favoring the death penalty.

A categorical statement is also called a proposition. Its distinctive character is that it asserts that something is the case or that something is not the case. Its assertion has a truth-value, that is, it may either be true or false.

a. components and structure – A categorical proposition follows the standard subject-copula-predicate form. The subject is introduced be a quantifier which specifies how much of the subject class is included in or excluded from the predicate class. The copula is expressed in the third person, present tense, of the verb to be.

All students majoring in philosophy are required to take Metaphysics and Epistemology.

quantifier: all

subject term: students majoring in philosophy

copula: are

predicate term: required to take Metaphysics and Epistemology

b. quantity of the proposition – refers to the extension of the subject. A proposition could be either universal [if it refers to all the members of the class designated by the subject term] or particular [if it refers to some members of the class designated by the subject term].

c. quality of the proposition – could be either affirmative [if the predicate is asserted of the subject – AffIrmo] or negative [if the predicate is denied of the subject – nEgO].

d. distribution in the predicate – the predicate of an affirmative proposition is undistributed [does not refer to all the members of the class designated] while the predicate of the negative proposition is distributed [refers to all the members of the class designated].

Meaning and Definition

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Over the years philosophers have held various conflicting views about the purpose of definition. For most logicians today, however, definitions are intended exclusively to explicate the meaning of words. A definition therefore is a group of words that assign a meaning to some word or group of words. It consists of two parts:

DEFINITION

definiendum

word to be defined

definiens

words that do the defining

1.Purposes of Definition

a. to increase vocabulary – There are situations when a deliberate explanation of the meaning of terms is required. To explain the meaning of a term is to give a definition to it. To understand what is being said, it is necessary to find out what the words mean and here a definition is required.

b. to eliminate ambiguity – it is not always clear what sense of a given word is intended. To resolve ambiguity a definition is required to specify the different meanings of the ambiguous word or phrase.

c. to reduce vagueness – Sometimes the limits of the applicability of the meaning of a term are not clear. There is a need for clarification and this is accomplished by giving a definition of the term that will permit a decision as to its applicability in a given situation where it was previously doubtful.

d. to explain theoretically – Technical terms carry a meaning of their own. To define is to elaborate the meaning that a term carries in a particular discipline like science among others.

e. to influence attitudes – There is a way to influence attitudes or stir the emotions and this is done by defining a term with a certain stant of meaning.

2.Classification of Definitions

a. stipulative definition – assigns meaning to new symbols.

b. lexical definition – reports the established usage of a term.

c. precising definition – helps to decide borderline cases of ambiguous meanings.

d. theoretical definition – attempts to formulate an adequate characterization of the objects to which it is applied.

e. persuasive definition – functions expressively to influence attitudes.

3.Techniques of Definition

DENOTATIVE	CONNOTATIVE
definition by giving examples or describing the objects being defined.	definition by genus and specific difference

Denotative Techniques – extensional – to define a term by indicating

the members of the class to which the definiendum refers.

a.1. by pointing them – demonstrative or ostensive – ex. A chair

means this, a table that; cafeteria here, infirmary there.

a.2. by naming them individually – enumerative – ex. Actor means

Gregory Peck, Tom Cruise, Antonio Banderas, Mel Gibson

a.3. by naming the individuals in group – subclass – ex. Vertebrate

means mammals, fishes, amphibians, birds; fiction means a poem,

novel, drama.

Connotative Techniques – intensional – to define a term by indicating the qualities or attributes that the world connotes.

1.by giving an equivalent term – synonymous – Physician means

doctor; Intentional means willful means deliberate.

To define by synonym requires that the definiens has the same intentional meaning as the definiendum. Also, the definiens must be simpler, more common or understandable in order to shed light on the definiendum. The following violate this last requirement: Concealed means clandestine or sob rosa. Esoteric means abstruse.

2.by specifying certain experimental procedures that determine

whether or not the word applies to a certain thing

- operational – ex. A solution is an acid if and only if litmus paper

turns red when placed in contact with it. One substance is

harder than another if and only if one scratches the other when

the two are rubbed together.

3.by identifying the genus and the specific difference. Genus

refers to a relatively large class to which the definiendum

belongs. Specific difference refers to the attribute which

distinguishes the definiendum from other members of the genus.

- ex. Ice is frozen water: Water is the genus and frozen is

the specific difference.

4.Rules for Defining

Rule 1	A definition should convey the essential meaning of the word being defined. Man is a rational animal / Man is being who smiles.
Rule 2	A definition should be neither too broad now too narrow. In some instances the context in which the definiens is used must be indicated. A school is a public institution of learning / A fish is an animal.
Rule 3	A definition must not be circular. The word to be defined should not be contained in the definition. A circle is a circular object. Silence means the state of being silent.
Rule 4	A definition should not be negative when it can be affirmative. Peace means harmony / Peace means the absence of war.
Rule 5	A definition should not be expressed in figurative, obscure, vague, or ambiguous language. A window is an orifice in an edifice to admit certain emissions of light energy. Faith is the substance of things hoped for, the guarantee of things unseen.
Rule 6	A definition should avoid affective terminology. Communism is the brilliant invention of Karl Marx and other foolish political visionaries in which the national wealth is supposed to be held in common by the people.

Fallacies of Ambiguity

2007-06-18T07:31:00.000-07:00

These fallacies, also called fallacies of clearness, occur in arguments whose formulations contain ambiguous words or phrases, whose meanings shift and change more or less subtly in the course of the argument and thus render it fallacious.

Equivocation - a fallacy committed when the conclusion of the argument depends on the fact that one or more words are used, either explicitly or implicitly, in two different senses in the argument.

A law can be repealed by legislative authority. The law of gravity is a law. Therefore, the law of gravity can be repealed by the legislative authority.

To identify the fallacy of equivocation, look for reasoning that involves a shift between two or more sense of a key word or phrase in the argument.

Amphiboly – this fallacy occurs when the arguer misinterprets a statement that is ambiguous owing to some structural defect and proceeds to draw a conclusion based on this faulty interpretation.

John told Bob that he had made a mistake. It follows that John has at least the courage to admit his own mistakes

Professor Johnson said that he will give a lecture about heart failure in the biology lecture hall. It must be the case that a number of heart failures have occurred there recently.

Amphiboly differs from equivocation in two important ways: 1) the former involves a structural defect in a statement while the latter is always traced to an ambiguity in the meaning of one or more words; 2) the former involves a mistake made by the arguer in interpreting an ambiguous statement made by someone else, whereas in the latter the ambiguity is typically the arguer’s own creation.

Composition – a fallacy committed when the conclusion of an argument depends on the enormous transference of a characteristic from the parts of something onto the whole. In other words, the fallacy occurs when it is argued that because the parts have a certain characteristic, it follows that the whole has the characteristic, too, and the situation is such that the characteristic in question cannot be legitimately transferred from the parts to the whole.

It is sometimes called the part/whole fallacy because the arguer mistakenly concludes that the whole must have some characteristics because each part or member has that characteristic. The structure of this fallacy is: each member of W is f. Therefore, W is f. The assumption of the argument is that what is true of the part is true of the whole. This is often false especially in those cases which the whole is more than the sum of its parts.

A feather is light. Therefore, a plastic containing a billion feathers is light.

Each member of the orchestra is excellent, so the orchestra is excellent.

Each player on this basketball team is an excellent athlete. Therefore, the team as a whole is excellent.

To recognize the fallacy of composition, look for an argument that moves from a claim about the parts or members of a group to a conclusion about the whole. Consider then whether it is justifiable to attribute what is true of the parts to the whole.

Division – a fallacy that is the exact reverse of composition. As composition goes from parts to whole, division goes from whole to parts. The fallacy is committed when the conclusion of an argument depends on the erroneous transference of a characteristic from a whole onto parts. Its structure is: W is f. Therefore, each member of W is f.

Salt is a nonpoisonous compound. Therefore, its component elements, sodium and chlorine, are non poisonous.

he union voted to strike. Therefore, every member of the union voted to strike.

Humans are the only animals capable of philosophical thinking. Thus every person is capable of philosophical thinking.

To recognize the fallacy of division, look for an argument that moves from a claim about a whole group or a group to a conclusion about one or all of the members of the whole. Then consider whether it is justifiable to attribute what is true of the whole to its parts.

Accent – a fallacy that arises from the mistaken interpretation of a statement but the mistake is due to the ambiguity in the way the statement is spoken. It occurs when the arguer illegitimately stresses one or more words in the given statement and then proceeds to draw a conclusion based on the resultant interpretation.

Catherine said (she) did not (drive) (her) (car) (today). Therefore: 1. Somebody else must have driven it; 2. She may have washed it; 3. She must have driven someone else’s; 4. She must have driven her truck; 5. She must have driven it yesterday.

A variation of the fallacy of accent occurs when the person who makes the original statement entices the arguer into a certain misinterpretation and thereby tricks him into construction a fallacious argument.

[The chief mate did not drink yesterday] [The captain is sober today.]

Fallacies of Relevance

2007-06-18T07:19:00.001-07:00

Informal Fallacies are typical errors or mistakes that arise commonly in ordinary discourse. They use persuasive arguments and so, although invalid, may appeal or come across as correct. They are then to be treated with caution in order to avoid the traps they set. We may technically define a fallacy as a type of an argument that may seem to be correct but proves, on examination, not to be so.

Fallacies of Relevance

When an argument relies on premises that are not relevant to its conclusion and therefore cannot be establish its truth. The connection between the premises and the conclusion is often emotional. In a good argument, it must be noted; the premises must provide genuine evidence for the conclusion.

Argumentum ad baculum – appeal to force – the use of threat in a form calculated to win the assent of another person or cause him to accept a conclusion. It is the discourse of power. The threat may either be physical or psychological so it is an argument based upon a threat. Arguers using this type of appeal try to persuade you by pointing out their powers over you or by warning you of the bad consequences of refusing to accept their argument.

Ladies and gentlemen of the jury, if you do not bring in a verdict of guilty, you may be this killer’s next victim!

We cannot have this statement on expenditures coming to the attention of the president. You have been the accountant here for nearly twenty years. It would be a shame to ruin all that now. I think it would be wise of you to take another look at the books.

To recognize the fallacy of appeal to force, look for the presence of a threat that is either explicit or subtly disguised.

Argumentum ad misericordiam – appeal to pity – when careful reasoning is replaced by devices contrived to cause sympathy or to evoke pity from another to get the other accept the conclusion. The basic structure of the argument is this: you should accept my conclusion out of pity. The arguer urges you to believe something by arousing your sympathy for him or his cause.

There is no question that what this young man did is intolerable and repugnant. He admits it himself. But you are not here to evaluate this man’s conduct morally; you are here to try him and determine his guilt or innocence. And as you think this over, I want you to think hard about this young man, his home life and his future, which you now hold in your hands. Think about his broken home, never knowing his father, being left by his mother. Think about the poverty he has known, the foster homes, the birthdays going unnoticed, and the Christmas he has never had. And think hard about what life in prison will do to him. Think about these things, and I know you will acquit him of this crime.

To recognize the fallacy of appeal to pity, look for premises that appeal to your sympathy.

Argumentum ad populum – appeal to the people or appeal to the emotion – careful reasoning is placed with devices aimed at creating enthusiasm and emotional support.

The basis structure of the argument is this: some statement S is true because most people believe S. It is, in effect, an appeal to commonly or traditionally held beliefs. The main error of this argument lies in the act that the popular acceptance of a policy does not show it to be wise. The fact that a great many people hold it to be true does not prove an opinion to be true.

To legalize jueteng or any other form of gambling because many people are engaging in it anyway.

To say that the constitution is defective because many people want it to be amended.

Direct: to excite the emotion and enthusiasm of the crowd. To arouse a kind of mob mentality. Not limited to verbal argumentation but also employs emotional charged phraseology.

political campaigns. slogans and labels.

Indirect: the appeal is addressed to one or more individuals separately. There is the bandwagon; the vanity – associating a product with a certain celebrity who is admired and pursued, the idea being that you, too, will be admired and pursued if you use it; and the snobbery type.

BANDWAGON:

90% are using Zest. You will be left behind or left out of the group if you do not use the product.

VANITY:

Only the ultimate in fashion could compliment the face of Cindy Crawford. Spectrum sunglasses – for the beautiful people in the jet set.S

SNOBBERY:

A Jaguar is not for everyone. If you think you belong to the select few, this distinguished classic may be seen and test driven at Ortigas Motor Cars. By appointment only, please!

To recognize the fallacy of appeal to the people, look for an argument in which the conclusion is based on assertions about commonly or traditionally held beliefs. The observation of Bertrand Russel is worth noting: In view of the silliness of the majority of mankind, a widespread belief is more likely to be foolish than sensible.

Argumentum ad hominem – attack against the person – when an attack is leveled not at the claim or conclusion of an opponent but at the person of the opponent. It is an attack upon the person rather than the persons’ ideas, on the opponent’s character implying that what he says should not be believed because of his character flaw. There are three common types of ad hominem arguments:

Abusive: when the attack is directly against a person seeking to defame or discredit him. It involves two claims: first, that the opponent possess a ceratin undesirable or negative characteristic and secondly, that the opponents’ words or abilities are not to be trusted because of that characteristic. The structure of this fallacy is: whatever anyone with undesirable characteristic X says is probably not true. Person A has undesirable characteristic X. Therefore, whatever A says is probably not true.

Well now, you have all heard Professor Clark tell us about the theory of evolution. But I am not surprised that he neglected to tell you that he is a godless atheist! How can this man speak the truth, I ask you?

To identify the ad hominem abusive fallacy, look for an attack on the person’s character rather than a person’s statements.

Circumstantial – when the attack is indirectly against persons suggesting that they adopt their view chiefly because of their special circumstances or interests. It implies that the opponent has special, usually self-interested, reasons for his or her claims. The argument attempts to refute the person’s statements not by offering reasons against it but by suggesting that the person himself does not have good reasons or honest motives for the position. The structure of this fallacy may be presented as follows: Person A has self-interested reasons for asserting S. Therefore, S is probably not true.

The auto industry lobbyists have been arguing that tax reform is unnecessary. But just remember this: it is the auto industry that stands to benefit the most if there is no change in the current tax laws.

To identify the ad hominem circumstantial fallacy, look for an argument that claims that the opponent advances his or her argument not because it is true but because the opponent has some other, usually ulterior, motive for wanting his or her argument accepted.

Tu quoque – Shifting the burden of guilt. It is an argument in which one defends oneself by accusing one’s attacker, usually of a similar wrongdoing. “Two wrongs do not make a right” so that even if the arguer is right in attacking his accuser, he has not defended himself against the charge.

Yes, I admit, I did lie to you about last night. But you have lied to me also before.

To identify the tu quoque fallacy, look for an argument that attempts to offer a defense by accusing the accuser of a similar wrongdoing.

The character of an individual is logically irrelevant to the truth or falsehood of what the person says. Abusive premises may persuade by the psychological process of transference. The field of emotional disapproval, when it is evoked, may be extended so as to include disagreement with the assertion the person makes. The same is to be said about assigning guilt by association. The circumstances of one who makes or rejects some claim have no bearing on the truth of that claim.

Argumentum ad verecundiam – appeal to authority – when the premises of an argument appeal to some party having no legitimate claim to authority in the matter at hand. This means, in other words, that the fallacy of appeal to authority occurs when the authority cited is not qualified in the relevant matters or, less typically, is not free from adverse influences. The argument in this case relies upon the assertions of someone who is not truly in a position to know.

According to my physics professor, Emily Dickinson’s poetry is for the birds.

That is good enough for me.

Marvis Frazier is America’s greatest boxer. I have that on the authority of Marvis’ father, Joe Frazier.

The underlying idea of such arguments is that some statement S is true because some authority A has said it is true. The argument’s basis structure is thus – authority A asserts that S. Therefore, S. Immediately this argument can be seen to be neither valid nor strong, since the mere fact that someone asserts S neither makes it so nor makes it probable. Typically, however, the arguer believes more than the mere fact that A asserts S. The arguer very likely is assuming such things as that A is someone who knows what he is talking about regarding S, or that A is speaking without basis , or that A is telling the truth. If those similar assumptions are well founded, the appeal to authority A may constitute good reasoning. Not all appeals to authority are fallacious. After all, we should accept the testimony of qualified and unbiased experts for we cannot be experts in every field ourselves.

To recognize the appeal to authority, look for an argument based primarily on the premise that some person or some publication reports that S is true. The fallacy occurs when the person or publication is not relevantly qualified or is not speaking without bias; in other words, whenever the truth of some proposition is assented on the basis of the authority of one who has no special competence in that sphere, the appeal to misplaced authority is committed.

Argumentum ad ignorantiam - appeal to ignorance – when it is argued that a position is true on the ground that it has not been proved false or vice-versa. The premises tell us that nothing can be known with certainty one way or the other about a certain subject while the conclusion states something definite. The two structures of the appeal to ignorance are: We do not know that S is false. Therefore, S is true or We do not know that S is true. Therefore S is false.

Well, I have examined all the arguments for the existence of God, and I have seen that none of them proves that God exists. That is reason enough for me: there is no God!

The lack of evidence that S is true (or not true) should not, in most cases, be taken as proof that S is not true (or true). However, there are at least two kinds of cases that resemble the appeal to ignorance in which a lack of evidence may justify the conclusion that S is true (or not true). In a court of law the failure to establish that a person has committed a crime is considered sufficient to allow us to conclude that the person is guilty. Thus, lawyers may argue that their clients are innocent because there is no evidence of their guilt. Notice, however, that finding a person innocent or guilty in a court of law is not a determination that the person did not commit the crime; it is a determination that the evidence does not justify a judgment of guilt. But if we conclude that a defendant did not commit the crime because he was found not guilty, we would be committing the fallacy of appeal to ignorance. Similarly, in scientific reasoning a failure to disconfirm or disprove a hypothesis lends support to the hypothesis, although it does not usually justify concluding that the hypothesis is true. Rather, each failure to disconfirm the hypothesis indicates that it is more probable.

Our ignorance to prove either the truth or falsity of a conclusion primarily signifies our inability and not the truth or falsity of the very conclusion. The fallacy of appeal to ignorance occurs when the lack of evidence or proof is not relevant to the conclusion but the arguer believes that it is.

To recognize the fallacy of appeal to ignorance, look for a conclusion based upon are absence of proof or evidence.

Accident – committed when a general rule is applied wrongly to a specific case. The general rule is cited in the premises and then wrongly applied to the specific case mentioned in the conclusion. Because of the accidental features of the specific case, the general rule does not fit.

Freedom of speech is a constitutionally guaranteed right,. Therefore, that radical communist should not be arrested for his speech that incited that riot last week.

Property should be returned to its rightful owner. That drunken marine soldier who is having a fight lent you his gun and he wants it back now. Therefore, you should return it to him now.

Converse Accident – hasty generalization – committed when a conclusion is drawn about all the members of a group from evidence that pertains to selected sample. The fallacy occurs when there is likelihood that the sample is not representative of the group. Such likelihood may arise if the sample is either too small or not randomly selected.

I have spoken to the members of the campus Siglakas club, and they prefer to use the activity fund for a film series on birds. So probably a majority of the two thousand students would prefer a film series on birds.

To identify the fallacy of hasty generalization, look for a conclusion that generalizes over a group. Notice whether the basis for the generalization is both representative of the group and sufficiently large to justify the generalization.

False Cause – committed whenever the link between premises and conclusion depends on some imagined causal connection that does not in fact exist. Any reasoning that relies on treating as the cause of a thing what is not really its cause is a fallacy – non causa pro causa. The most common variety of false cause is the error of concluding that an event is cause by another simply because it follows the other – post hoc ergo propter hoc.

A black cat crossed my path and later I tripped and sprained my ankle. It must be that black cats are really bad luck

During the past two months, every time that the cheerleaders wore blue ribbons in their hair, the basketball team was defeated. Therefore, to prevent defeats in the future, the cheerleaders should get rid of those blue ribbons.

There are more laws in the books today than ever before, and more crimes are being committed than ever before. Therefore, to reduce crime we must eliminate the law.

Another type of fallacy of false cause is called oversimplification. This occurs when an arguer explains the occurrence of some event or phenomenon in terms of one or more of its least important causes.

I blame the television media for the epidemic of hijackings, kidnappings, and other acts of terrorism. If we would stop televising terrorist acts, they would stop.

To identify the fallacy of false cause, look for the claim that one thing or event is cause by or explained as the result of some other thing or event A. Then consider whether there is any good evidence that A causes B. The variation called oversimplification can usually be spotted when an arguer proposes a solution to a problem while at the same time overlooking other causal factors.

Petitio principii – begging the question – assumes the truth of what one seeks to prove, in the effort to prove it. Phrasing the argument so that the premise and conclusion say the same thing in two slightly different ways. Another name for this is circular argument. The argument begs the question at issue because it asks that the statement to be proved be granted beforehand. It assumes as true the very point in question.

Philosophers are highly intelligent individuals because if they were not highly intelligent they would not be philosophers.

The Bible asserts that God exists. The Bible is the divine word of God. Therefore, God exists.

It is plain to see that suicide is morally wrong because, as any thinking person will admit, no one is ever justified in taking his or her own life.

To recognize the fallacy of begging the question, look for an argument that assumes already the very issue under debate. Be aware that a question-begging argument may appear to offer legitimate, independent support, but on closer examination a premise in fact either itself rests upon the conclusion or restates the conclusion in different words.

Complex question – when a single question that is really two or more questions is asked and the single answer is then applied to both questions.

Have you stopped cheating on your girlfriend?

If respondents are not sophisticated enough to identify a complex question when one is put to them, they may answer quite innocently and be trapped by a conclusion that is supported by no evidence at all.

False analogy – a fallacy committed when the analogy is not strong enough to support the conclusion that is drawn. It draws a conclusion about something on the basis of an analogy with or resemblance to some other thing. The assumption is that if two or more things are alike in some respects, they are alike in some other respect. The structure of the argument is as follows: A and B are both f, g, and H. A is also j. Therefore, probably B is j.

Harper’s new car is bright blue, has leather upholstery, and gets an excellent mileage. Crowley’s new car is also bright blue and has leather upholstery. Therefore, it probably gets excellent mileage too.

To recognize the fallacy of the false analogy, look for an argument that draws a conclusion about one thing, event, or practice on the basis of its analogy or resemblance to other. The fallacy occurs when the analogy or resemblance is not sufficient to warrant the conclusion, as when, for example, the resemblance is not relevant to the possession of the inferred feature or there are relevant dissimilarities.

Slippery slope – this a variety of the false cause fallacy. It occurs when the conclusion of an argument rests upon the claim that a certain event will set off a chain reaction, leading in the end to some undesirable consequence, yet there is no sufficient reason to think that the chain reaction will actually take place.

Attempts to outlaw pornography threaten basic civil rights and should be summarily abandoned. If pornography is outlawed, censorship of news papers and news magazines is only a short step away. After that there will be censorship of textbooks, political speeches, and the content of lectures delivered by university professors. Complete mind control by the central government will be the inevitable result.

You have all heard of grade inflation. Well, I want to speak to you about grade depression: the serious harm we do to students by grading them too hard rather than too easily. What does it do to students to measure them by too strict a standard? It frustrates them. It conditions them to expect failure. They recoil from responsibility, always taking the easy route rather than learning to challenge and hence improve themselves. They develop habits of dependency, and many develop the symptoms of neurosis and other psychological disorders. Can we afford a generation of weak, dependent people unsuited for the demands of contemporary society?

To recognize the slippery slope fallacy, look for an argument claiming that a certain practice or event will initiate a series of events ultimately leading to some undesirable consequences.

Red herring – a fallacy that is committed when the arguer diverts the attention of the reader or listener by addressing a number of extraneous issues and ends by presuming that some conclusion has been established. The fallacy got its name from the practice of using a herring, a particularly smelly fish when cooked, to divert hunting dogs from the scent of a fox. To commit the fallacy of red herring in an argument is to draw attention away from an issue by raising some other, seemingly related issue. In so doing, the arguer attempts to sidetrack the opponent’s argument.

Friends and neighbors I urge you to defeat the proposal to make jail sentences mandatory for drunk drivers. My opponent claims that it will reduce the number of accidents caused by drunk drivers. But if we really want to reduce traffic accidents, then we should stand behind those men and women whose chief responsibility is our safety. I am referring of course, to our valiant police officers, what we need to is increase their salaries, beef up the police force, and, most importantly, stop butting into their business with troublesome people.

I agree with my opponent that pornography is a national problem, and I am almost persuaded by his argument that women are being degraded and victimized by pornography. I say, almost persuaded… until I remember the facts that my opponent obviously overlooks: namely, that the people of South Africa are not merely degraded and victimized, they are deprived of every right due a human being. And what I do not understand is how we convince ourselves that our so called national problem takes precedence over genuine oppression and suffering.

To recognize the fallacy of red herring, look for an argument in which the speaker responds by directing attention away from the issue to other, seemingly related issues.

Suppressed evidence – a fallacy committed when an arguer ignores evidence that would tend to undermine the premises of an otherwise good argument, causing it to be unsound or uncogent. Suppressed is a fallacy of presumption and is closely related to begging the question. As such, its occurrence does not affect the relationship between premises and conclusion but rather the alleged truth of the premises. The fallacy consists in passing off what are at best half-truths as if they were the whole truth, thus making what is actually a defective argument appear to be good. It is especially common among arguers who have a vested interest in the situation to which the argument pertains.

The second amendment to the constitution states that the right of the people to keep and bear arms shall not be infringed. But a law controlling handguns would infringe on the right to keep and bear arms. Therefore, a law controlling hand guns would be unconstitutional.

Deduction and Induction

2007-06-18T07:14:00.000-07:00

Arguments are traditionally divided into two different types, deductive and inductive.

A deductive argument is one in which the conclusion follows necessarily from the premises; in other words, the premises support the conclusion in such a way that if they are assumed true, it is impossible that the conclusion be false.

An inductive argument is one in which the conclusion follows only probably from the premises; in other words, the premises support the conclusion in such a way that if they are assumed true, then, based on that assumption, it is only probable that the conclusion be true.

Three factors that bear upon the evaluation of an argument is inductive or deductive are the following:

· the occurrence of special indicator words – If, in drawing a conclusion the arguer uses words such as “probable,” “improbable,” “plausible,” “implausible,” “likely,” “unlikely,” or “reasonable to conclude,” the evaluator may take such indicators as reason for considering the argument inductive.

Neon has unstable isotopes. Therefore, since argon is similar in may ways to neon, it probably follows that argon has unstable isotopes, too.

On the other hand, if the arguer uses words such as “necessarily,” “certainly,” “absolutely,” or “definitely,” the evaluator may consider the argument deductive.

If a substance is a noble gas, it is inert. Therefore, since argon is a noble gas, it necessarily follows that it is inert.

· the nature of the inferential link between premises and conclusion – If this link is such that the conclusion follows necessarily from the premises, the argument is clearly deductive. To say that the conclusion follows “necessarily” means that the premises support the conclusion in such a way that if they are assumed true, it is absolutely impossible that the conclusion be false.

All saleswomen are extroverts. Judy Wage is a saleswoman. Therefore, she is extrovert.

On the other hand, if the conclusion does not follow necessarily from the premises but does probably, it is usually best to consider the argument inductive.

The vast majority of saleswomen are extroverts. Rose Liam is a saleswoman. Therefore, Rose Liam is an extrovert.

· The character or form of argument the arguer uses – Sometimes it happens that an argument contains no indicator words and the conclusion follows neither necessarily nor probably from the premises, that is, the premises provide no clear support for the conclusion, This situation points out the need for the third factor to be taken into account, which is the character or form of argumentation the arguer uses.

Five such types of argumentation that are typically deductive are the following:

Argument based on mathematics

An argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement.

A shopper may place two apples and the three oranges into a paper bag and then conclude that the bag contains five fruits. /A surveyor might measure a square piece of land and, after determining that it is 100 feet on each side, conclude that it contains 10,000 square feet.

Argument from definition

An argument in which the conclusion is claimed to depend upon the definition of some word or phrase used in the premise or conclusion.

Claudia is mendacious, so she tells lies. / This paragraph is prolix, so it follows that it is excessively wordy.

Categorical syllogism

A syllogism in which each statement begins with one of these quantifiers: “all,” “no,” “some.”

All lasers are optical devices. Some lasers are surgical instruments. Therefore, some optical devices are surgical instruments.

Conditional syllogism

A syllogism having a conditional statement for one or both of its premises.

If quartz scratches glass, then quartz is harder than glass. Quartz scratches glass. Therefore, quartz is harder than glass.

Disjunctive syllogism

A syllogism having a disjunctive statement (“either… or”) for one or both of its premises.

Either breach of contract is a crime or it is not punishable by the state. Breach of contract is not a crime. Therefore, it is not punishable by the state.

The following are typically inductive forms of argumentation. Inductive arguments are such that the content of the conclusion is in some way intended to go beyond the content of the premise. The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about.

Prediction

The premises deal with some known event in the present or past, and the conclusion moves beyond this event to some event in the relative future.

Because certain meteorological phenomena have been observed to develop over a certain region in the Pacific, a storm will occur there in the next several hours.

Argument from analogy

An argument that depends on the existence of an analogy, or similarity, between two things or state of affairs. Because of the existence of this analogy, a certain condition that affects the better known thing or situation is concluded to affect the similar lesser known thing or situation.

From knowledge that his Mercedes car is an expensive car, I argue that your car, being a Mercedes, is also expensive.

Inductive generalization

An argument that proceeds from the knowledge of selected sample to some claim about the whole group. Because the members of the sample have a certain characteristic, it is argued that all the members of the group have the same characteristic.

One may argue that because three oranges selected from a certain crate were especially tasty and juicy, all the oranges from that crate are especially tasty and juicy.

Argument from authority

An argument in which the conclusion rests upon a statement made by some presumed authority or witness.

A lawyer may argue that the criminal committed no murder because an eyewitness testified to that effect under oath.

Argument based on signs

An argument that proceeds from the knowledge of a certain sign to knowledge of the thing or situation that the sign symbolizes.

When driving on an unfamiliar highway, one might see a sign indicating the road makes several sharp turns one mile ahead. Base on this information, one might argue that the road does indeed make several sharp turns one mile ahead.

Causal inference

An argument that proceeds from knowledge of a cause to knowledge of the effect or conversely, from knowledge of an effect to knowledge of a cause.

From the knowledge of the bottle of wine had been accidentally left in the freezer overnight, someone might concluded that it had frozen (cause to effect) Or, after tasting a piece of chicken and finding it dry and crunchy, one might conclude that it had been overcooked. (effect to cause)

Although every argument involves the claim that its premises provide evidence for the truth of its conclusion, only a deductive argument involves the claim that its premises provide conclusive evidence. In the case of deductive arguments the technical terms valid and invalid are used in place of correct and incorrect. A deductive is valid when its premises, if true, do provide conclusive evidence for its conclusion, that is, when premises and conclusion are so related that it is absolutely impossible for the premises to be true unless the conclusion is true also. Every deductive argument is either valid or invalid. The task of deductive logic is to clarify the nature of the relation between premises and conclusion in valid arguments, and thus to allow us to discriminate valid and invalid arguments.

An inductive argument, on the other hand, involves the claim, not that its premises give conclusive evidence for the truth of its conclusion, but only that they provide some evidence for it. Inductive arguments are neither valid nor invalid in the sense in which those terms are applied to deductive arguments. Inductive arguments may, of course, be evaluated as better or worse, according to the degree of likelihood or probability, which their premises confer upon their conclusions.

Diagramming Arguments

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Diagramming Arguments – Another way to expose an argument is to diagram it. To do this, first read through and number each statement in sequence. Then draw an arrow from the statement number of the premise to the number of the conclusion as follows.

Single support:

[1] The branch manager was promoted to company vice president; therefore,

[2] he will transfer to the main office.

1-------->2

The diagram shows that statement 1 is the only support offered for the conclusion in statement 2.

Joint support:

[1] If the branch manager is promoted to vice president of the company, then he will transfer to the main office. [2] He is bound to be promoted. [3] So, he will be transferring to the main office.

1 + 2------->3

This argument offers two premises for concluding that 3. Moreover, the premises operate together in support of the conclusion. Premise 1 does not provide reason for 3 without being joined with 2. This is called joint support and their dependence is indicated by the + sign.

Independent support:

[1] Cats make good pets because [2] they are affectionate. [3] They are clean. [4] They are entertaining and [5] they do well in apartments.

The conclusion is statement 1. Notice that four distinct premises are offered in support and that these premises do not need one another to provide support. This is called independent support.

2------------>

3------------>

4----------->

5----------->

Joint support should not be confused with independent support. A premise provides independent support if it does not need another premise or is not needed by another premise to support the conclusion. Otherwise it provides joint support along with another premise.

Extended argument:

[1] Cats make good pets because [2] they are affectionate. [3] They are clean. [4] They are entertaining and [5] they do well in apartments. So , [6] if you want a good pent, you should get a cat.

Premises 2 through 5 support the conclusion 1. From that conclusion it is further concluded that 6.

2------------->

3------------>

1----------> 6

4------------>

5------------>

This is called an extended argument because it contains an argument within an argument.

Cats make good pets and cats make good anatomical subjects. Therefore, some good pets make good anatomical subjects. Since good anatomical subjects are in high demand in medical schools, it follows that some good pets are in high demand in medical schools.

1+ 2--------> 3 + 4--------> 5

Above we see that premises 1 and 2 support 3. Statement 3 is then combined with 4 to support the conclusion 5

Identifying Non-arguments

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One way to facilitate the recognition of arguments is to distinguish them from nonarguments. This is not easy especially when a passage contains no argument indicators. For such a passage could simply be a series of unsupported assertions rather than an argument. The following are typical kinds of nonarguments:

Warnings – discourses aimed at modifying someone’s behavior. If no evidence or reason is given to prove that someone should do something or avoid doing something then there is no argument.

Let everyone know that no mercy shall befall any violator of the law in this country.

Statements of belief or opinion – expressions of what someone happens to believe or think at a certain time. When no evidence or reason is given to prove that what the author thinks is true is no argument.

I think a nation such as ours, with its high moral traditions and commitments, has a further responsibility to know how we became drawn into this conflict, and to learn the lessons it has to teach us for the future. [Alfred Hassler, Saigon]

Description – consists of one or more statements that, taken together, cause a certain picture to appear in the mind of the reader.

At Rajghat, a few hundred feet from the river, a fresh pyre had been built of stone, brick and earth. It was eight feet square and about two feet high. Long, thin sandalwood logs sprinkled with incense were stacked on it. Mahatma Gandhi’s body was lay on the pyre with his head to the north. In that position Buddha had met his end. [Louis Fisher, Gandhi: His Life and Message for the World]

Report – a group of statements that conveys information about some situation or event.

“56,000 curies of radioactive tritium were accidentally released from the Savanna River nuclear weapons plant in South Carolina. A spokesman for the plant said that the radiation posed ‘no health hazard to the public’ since it was ‘equivalent to the amount that would be received on a 30-minute jet flight at 36,000 feet’”.

Expository passage – It often happens that an author will begin a paragraph with a topic sentence and then go on develop it. The author’s aim is not to prove the topic sentence but merely to expand or develop it.

There is a stylized relation of artist to mass audience in the sports, especially in baseball. Each player develops a style of his own – the swagger as he steps to the plate, the unique windup a pitcher has, the clean-swinging and hard-driving hits, the precision quickness and grace of infield and outfield, the sense of surplus power behind whatever is done.

The aim of this of this passage is not so much to prove that the first statement is true as it is to flesh out the notion of a stylized relation to a mass audience.

Illustration – Consists of a statement about a certain subject combined with a reference to one or more specific instances intended to exemplify that statement. Illustrations are often confused with arguments because many of them contain indicator words.

Chemical elements, as well as compounds, can be represented by molecular formulas. Thus, oxygen is represented by “O2”, sodium chloride by “NaCl”, and sulfuric acid as “H2SO4”.

Many scientists turn to music for rest and relaxation. Thus Albert Einstein played the violin.

The above passages are not arguments because there is no claim that anything follows from evidence. The purpose of the word “thus” is not to indicate that something is being proved but merely to show how something is done.

Comparison – compound statements that point out a similarity between two events or instances.

Just as normal men would die without water, so Jack would die without wine.

Conditional – an “if… then…” statement. Every conditional statement is made up of two component statements. The statement immediately following the “if” is called the antecedent and the other following the “then” is called the consequent.

Conditional statements are not arguments for the following reason: in an argument the premises are asserted to be true, and the conclusion, because it is claimed to follow from the premises, is also asserted to be true. In a conditional statement, on the other hand, neither the antecedent nor the consequent is asserted as true. What is asserted is that if the antecedent is true, then the consequent is true. But while no single conditional statement is an argument, a conditional statement may serve as either the premise or the conclusion of an argument.

If cigarette companies publish warning labels, then smokers assume the risk of smoking.

Cigarette companies do publish warning labels.

Therefore, smokers assume the risk of smoking.

Conditional statements are very important in logic because they are use to express the relationship between necessary and sufficient conditions. An event A is said to be sufficient condition for an event B whenever the occurrence of A is all that is required for the occurrence of B. A sufficient condition for increasing one’s heart rate is running 1,000 yards.

On the other hand, an event B is said to be a necessary condition for an event A whenever A cannot occur without the occurrence of B. A necessary condition for watching television is opening your eyes.

Temporal sequence – besides its logical sense, the premise indicator since has a temporal meaning which is sometimes mistakenly interpreted as an argument but is really a way of saying simply that in the period of time following an event several others subsequently happened.

Since Marilyn Monroe died, men have walked the moon.

Recommendation – Although it uses the term therefore and similar terms, a recommendation is not an argument. It does not establish a claim but only cites basis for the action prescribed.

I have no misgivings regarding the professional competence and the moral integrity of the applicant. I therefore recommend him for your favorable consideration.

Explanations – Every explanations is composed of two distinct components: the explanandum and the explanans. The former is the statement that describes the event or phenomenon to be explained, while the latter is the state or group of statements that purports to do the explaining. Explanations are sometimes mistaken for arguments because they often contain the indicator word because. Yet explanations are not arguments for the following reasons; in an explanation, the explanans is intended to show why something is the case, whereas in an argument the premise are intended to prove that something is the case

The Challenger spacecraft exploded after liftoff because an O-ring failed in one of the booster rockets.

The sky appears blue from the earth’s surface because light rays from the sun are scattered by particles in the atmosphere.

Cows can digest grass, human cannot, because their digestive systems contain enzymes not found in humans.

There a number of clues to help whether an argument or an explanation is being offered.

1.) The conclusion of an argument is generally something regarded by the arguers in need of support while the premises are regarded as already will known. In an explanation, on the other hand, the fact being explained is generally regarded as already well established, while the explanatory factors cited are often highly speculative.

2.) When because or similar terms are used an explanation indicators, they can be replaced without change of senses with as a result of or due to.

3.) When modified by adverbs like definitely, probably, and possibly or by conjunctions like “either-or” or “not-but” because can only be interpreted as an explanation indicator.

The missing plane crashed, because an instrument malfunctioned.

The missing plane crushed because the wreckage was found.

Recognizing Non-arguments

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Recognizing Arguments – Not all passages contain arguments. One aim of logic is to distinguish passages that contain arguments from those that do not. In general, a passage contains an argument if it claims to prove something. If it does not do so then it does not contain an argument. Two conditions must be fulfilled for a passage to claim to prove something.

1.) At least one of the statements in the passage must present evidence or reasons for something.

2.)There must be a claim that the evidence or reasons supports something.

Because objects of art are expressive, they are a language.

The proposition Objects of art are expressive is asserted as evidence or reason (premise), and the proposition They are a language is claimed as supported (conclusion) by the evidence of the reason.

Although every passage expressing an argument contains several propositions asserted in it, not every passage in which several propositions are asserted need contain an argument. For an argument to be present, one of the asserted propositions must be claimed to follow from other propositions asserted to be true, which are presented as grounds of, or reasons for believing, the conclusion. This claim may be either explicit or implicit. It may be made explicit by the use of premise indicators or conclusion indicators or by the occurrence of such words as must, should, ought, or necessarily in the conclusion. But the presence of these argument indicators is not always decisive.

Since Henry graduated from medical school, his income is probably very high.

Since Henry graduated from medical school, there have been many changes in medical techniques.

The first argument is an argument but the second is not although both make use of the premise indicator since. The basic structure of the argument can be illustrated thus:

Q because P

If we are interested in establishing the truth of Q, and P is offered as evidence for it, the Q because P formulates an argument. However, if we regard the truth of Q as being unproblematic, as being at least well established as the truth of p, but are interested in explaining why Q is the case, the Q because P is not an argument but an explanation.

Premise and Conclusion

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Premise and Conclusion – The terms premise and conclusion denote a function. Thus no proposition taken by itself can be a premise or a conclusion. They are such only within the context of an argument. An argument may be diagrammed simply as follows:

Premise/s--------------------------------> Conclusion

What serves as the evidence what is supposed to follow from the evidence

Premise and conclusion are relative terms. One and the same proposition can be a premise in one argument and a conclusion in another.

All mammals feed their young with milk.

All human are mammals.

Therefore, all humans feed their young with milk.

All that feed their young with milk are mammals.

All humans feed their young with milk.

Therefore all humans are mammals.

There are clues one can use to pick out the conclusions and the premises of an argument. Certain words in our language may be used to signal conclusions or premises. They are called indicators.

PREMISE INDICATORS		CONCLUSION INDICATORS
Since, as indicated by, because, for, in that, may be inferred from, as, seeing that, for the reason that, inasmuch as, given that, may be concluded from, or the reason that, due to the fact that		Therefore, wherefore, accordingly, we may conclude, entails that, hence, thus, consequently, we may infer that, it must be that, whence, so, it follows that, implies that
Premise	Shows that Indicates that Proves that Entails that Implies that Establishes that		Conclusion
Conclusion	Is shown by Is indicated by Is proven by Is entailed by Is implied by Is established by		Premise

An argument is seen more clearly if it is written out in argument form. In this format, the premises are listed first, followed by a solid line separating them from the conclusion, listed at the bottom. Each statement is numbered and the form is as follows:

The president, being human, is mortal, as all human beings are mortal.

Premise 1

Premise 2

-----------

Conclusion

All human beings are mortals.

The president is a human being.

--------------------------------------

Therefore, the president is mortal.

God does not exist because if he did there would be no suffering and evil in the world; but obviously suffering and evil do exist. Thus, there is not God.

Premise 1

Premise 2

------------

Conclusion

If God existed there would be no suffering and evil in the world.

But obviously suffering and evil do exist.

---------------------------------------------------------------------------

Therefore, there is no God

Exposing the Argument

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Exposing the Argument – To expose an argument is to pick out the conclusion and the premise or premises. It is easier to identify the conclusion. It is the claim being made. The premise is the reason to back up the claim.

Sharks are not mammals since no fish is a mammal and sharks are fish.

If the president were really doing his job, the budget deficit would be reduced. But the budget deficit has not been reduced. So the president is not really doing his job.

It must be noted that a conclusion is not a mere summary of the premises. It does not simply restate the premise. The key point is inference – the process by which one proposition is reached and affirmed on the basis of one or more other propositions accepted as the starting point of the process. An argument is neither just a sequence of statements nor simply a narrative of a temporal sequence of events.

It is sunny today. It is also the beginning of the week.

Since the time he graduated from college he has not slowed down in his effort to become financially stable and so he has been working long hours and is now reaping the fruits of his labor.

It is important to distinguish conclusions from unsupported claims. Reasons must be offered for accepting a statement before we can classify it as the conclusion of an argument. Unsupported claims may be true but we will have to look elsewhere for reasons to believe them.

Proposition and Argument

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Propositions – Propositions are statements which constitute the basic element in reasoning. Their distinctive character is that they assert that something is the case or that something is not the case. Their assertion may be true or false. Propositions are therefore statements that have a truth-value, that is, they have the property of being true or false.

Logic is the study of the principles of correct reasoning.

Being a president is like riding a tiger.

Charles Dickens wrote Romeo and Juliet.

Propositions differ from question, commands, and examinations. Only propositions can be either affirmed or denied. Questions may be asked, commands given, and exclamations uttered, but none of them can be affirmed or denied, or judged to be either true or false.

Argument – Argument is a group of statements, one of which is claimed to follow from the others.

1.) An argument consists of at least two statements, one that is claimed to follow, called the conclusion, and at least one another, called the premise, that is claimed to support the conclusion.

2.)Every argument involves at least one inference – the inference from the premise to the conclusion.

3.) An argument involves a claim that one statement follows from the others, that is an argument purports to show that something is true.

An argument therefore is not a mere collection of propositions but contains a premise-conclusion structure. The simplest kind of argument consists of just one premise and a conclusion. Here is an example in which each is stated in a separate sentence:

The investigation of supernatural phenomena lies outside the realm of science. Therefore science can neither prove nor disprove the existence of God.

In the above example the premise is stated first and the conclusion second. But the order in which they are stated is not significant from the point of view of logic. An argument in which the conclusion is stated in the first sentence and the premise in the second is shown by the following example.

Moreover, cutting social security will not improve the deficit problem. As the chairman of the National Economic Development Authority has noted, social security is funded by separate payroll taxes and contributes not a cent to the deficit.

In some arguments the premise and the conclusion are stated in the same proposition. Following is an example of a one-sentence argument whose premise precedes its conclusion.

The solar system is much younger than the universe (only 4.5 billion years compared with 10 to 15 billion years), and so it must have formed from older matter that had a previous history.

Sometimes the conclusion precedes the premise in a one-sentence argument, as in the following example.

The budget deficit will not be brought under control because to do so would require our elected leaders in Congress to do the unthinkable – act courageously and responsibly.

As a general rule, when someone gives reasons to support a point of view, that person is usually offering an argument. Likewise when reasons are offered in an effort to persuade us to perform a specified action, we are presented with what is in effect an argument even though the conclusion may be expressed as an imperative or command.

Wisdom is the principal thing; therefore seek the pursuit of wisdom.

Neither a borrower nor a lender be; For loan oft loses itself and a friend.

An argument is good if the conclusion follows from the premises while an argument is bad if the conclusion does not really follow although it is intended to.

Identical twins who inherit the same genes have different intelligence quotient. Environment must play a role in determining intelligence.

A comet appeared and the locusts came. There must be a connection between the appearance of a comet and the coming of the locusts.

Logic and Inference

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Logic – Logic can be defined as the science of correct reasoning. As a science, it employs in an orderly manner certain laws or rules and methods whereby we may derive a valid conclusion from a given set of facts or ideas. Its purpose is to develop a science of reasoning. It clarifies our thinking and helps us to evaluate the reasoning behind the systems of belief and theories that we encounter in life. Logic helps us to understand what our beliefs mean, how to express them clearly, and how they may be supported.

Sometimes the word Logic is used in a loose sense, as in the following statements:

Sociologists understand the logic of events.

The logic of his argument is difficult to criticize.

The logical thing for you to do is go into law.

Socrates is a very logical person.

In our course however, we refer to Logic in a technical sense, namely, as a scientific way of determining the correctness of our thinking.

Logic is about reasoning and reasoning is a kind of thinking. It is a kind of thinking in which we try to solve a problem, make a decision, or determine what is true. It is thinking with a purpose which is to arrive at a conclusion. This process is called inference.

Inference - Inference is the process by which one proposition [conclusion] is reached and affirmed on the basis of one or more other propositions [premises] accepted as the starting point of the process.

Reasoning involves inference. The mind draws a conclusion from a given premise, based on an inferential connection between these statements. Reasoning expresses a logical movement from one statement to another.

The birds are flying south. Winter must be coming.

The lights are out and their car is gone. I suspect they are not home.

Raisins are dried grapes. Prunes are dried plums.

She graduated summa cum laude. She must have studied hard in college.

The cat is standing by her dish meowing. She is probably hungry.

These are some of the symptoms of neurosis: strong guilt feeling, irrational fears, insomnia, and inability to make decisions.